On the structure of countable hyperspaces of regular subcontinua
Year: 2026
Type: preprint
Abstract: Main result. If X is a metric continuum whose hyperspace D(X) of regular subcontinua is countable, then D(X) is a Gδ subset of C(X), hence completely metrizable and scattered, with dense isolated points. In particular D(X) is never homeomorphic to the rationals. This answers the rational case of a question of Ramírez Angarita (2023, Pregunta 3.2.14) and of Camargo, Ordoñez and Ramírez (Appl. Gen. Topol. 25 (2024), Question 3.26); the irrational case was answered in the companion repository. Every theorem of the paper is formalized in Lean 4 with Mathlib
Author: Alves de Almeida, Lucas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225815461
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